The SED analysis relies on the following distances and photometry. The distances were estimated based on the parallaxes provided in Gaia EDR3 ([1]}). Following [2]}, the inverse of the parallax was used to estimate the distances when the fractional parallax error (fpe) was smaller than 0.1. A Bayesian method with a geometric prior from [2]} was used to derive the distances in case fpe > 0.1, or when the parallax was negative. The distances for the 209 HAeBes in the sample are listed in Col. 4 of Table REF . In addition, we assumed that a low-quality parallax and thus a potentially spurious distance can be obtained when any of the following criteria based on Gaia EDR3 parallaxes, uncertainties and quality flags are met: First, negative parallax or fpe > 1. Second, renormalised unit weight error (RUWE) > 3. Third, astrometric_excess_noise > 0.5 and astrometric_excess_noise sig > 2. Finally, RUWE > 1.4 and ipd_gof_harmonic_amplitude > 0.1. The last three criteria were defined according to Table 4 of [1]} and Sect. 3.2 of [5]}. The 42 objects indicated with the dagger in Table REF  have low-quality parallaxes according to the criteria listed above. Although we also derived the stellar and circumstellar properties of these objects, they were not considered in the analysis (Sect. ). The potential spuriousness of Gaia EDR3 astrometric solutions is subject of ongoing work, for which we adopted conservative criteria. For instance, essentially all stars with low-quality parallaxes based on the very recent work by [6]} (not yet submitted, according to the astro-ph notes) are also identified here, although roughly half of the sources with low-quality parallaxes according to our criteria are not classified as such based on [6]}.
